Solve the inequality and express your answer in interval notation. x^2-12x+3<0

Solve The Inequality And Express Your Answer In Interval Notation. X^2-12x+3&lt;0

Answers

Answer 1

Solution:

B.) [tex](6-\sqrt{33}, 6+\sqrt{33})[/tex]

Hope this helps! If so, please lmk! Thanks and good luck!


Related Questions

Find the nth term, the fifth term, and the 100th term, of the arithmetic sequence determined by a = 2 and d = 3​

Answers

Answer: an=3n-1    a₅=14   a₁₀₀=299

Step-by-step explanation:

a=2     d=3

[tex]\boxed {a_n=a_1+d(n-1)}\\\\a_n=2+3(n-1)\\\\a_n=2+3n-3\\\\a_n=3n-1\\\\a_{100}=3(100)-1\\\\a_{100}=300-1\\\\a_{100}=299\\\\a_5=3(5)-1\\\\a_5=15-1\\\\a_5=14[/tex]

19 more than four times a number is equal to the difference between -86 and three times the number find the number

Answers

Answer:

the number is -15

Step-by-step explanation:

if you turn the word problem into an equation it would be

4x+19=-86-3x

with x being the unknown number

the next step is to move the -3x to the other side by adding it to the 4x

your equation should now be 7x+19=-86

next you should move the 19 to the other side by subtracting it from the -86

this leaves you with the equation

7x= -105

lastly you must divide the -105 by seven which leaves you with the answer x= -15

Decide whether the table shows a proportional relationship between x and y.

x y
17 2 5/6
5/6 5/36
6 1/6
19 3 1/6

Answers

The table shows a proportional relationship between x and y.

In this question, we have been given a table which contains values of x and y.

We need to decide whether the table shows a proportional relationship between x and y.

x             y

17         2 5/6

5/6       5/36

6            1/6

19          3 1/6

First we convert the improper fraction in the y-column to proper fraction.

2 5/6 = 17/6

and 3 1/6 = 19/6

so, given table would be,

x             y

17          17/6

5/6       5/36

6            1/6

19          19/6

Consider the ratio x/y of each row:

x             y                x/y

17          17/6            1/6

5/6       5/36            1/6

6            1/6              1/6

19          19/6             1/6

As the ratio x/y is constant, x and y are directly proportional.

Therefore, the table shows a proportional relationship between x and y.

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22 out of 25
math students
bring their
calculators to
class how many
students would
have a
calculafors in a
group of 80
math students

HELP PLEASE

Answers

I think it’s 66 :) please put best

XZ is the perpendicular bisector of segment WY. Solve for m. Enter a NUMBER only.

Answers

2(14m-8)=180

24m-16=180

24m=196

m= 8 and 1/6

the estimate closest to the length of a pen​: ​30cm, 160​mm, or 16 mm.

Answers

Answer:

160 mm.

Step-by-step explanation:

the average pen is 149mm. the average pen is 14.9cm. 160mm is closest.

It would have to be the 160mm.

This is because store-bought pens average 130 and 140mm/ 13 – 14 cm. This is closely followed by pens in the 140 – 150mm range.

Hope this helps!

Have a great day and God bless! :)

HELP PLEASE DUE TODAY

Answers

12) Z ∪ N = {Set of Integers}

13)  H ∪ Q = R which is a set of real numbers

How to classify numbers?

We are told that;

R = U represents the set of real numbers

N is the set of natural numbers

W is the set of whole numbers

Z is the set of integers

Q is the set of rational numbers

H is the set of irrational numbers

12) We want to find Z ∪ N. This is a set union of the set of integers and the set of natural numbers.

A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero. Thus, an integer is also a rational number and all natural numbers are positive integers and as such;

Z ∪ N = {Set of Integers}

13) We want to find H ∪ Q. This is a set union of the irrational numbers and the set of rational numbers. Now, we know that all real numbers are classified as either rational or irrational numbers

Thus; H ∪ Q = R which is a set of real numbers

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find inequality : JoJo can eat no more than 25 carbs per meal. Which inequality describes JoJo's situation?

Answers

Answer:

Jojo is on a low carb diet

thank you so much for the help!!

Answers

The independent variable in these equations based on how they are written is x, since y is a function of x here so y depends on the value of x, while x can be changed freely.

So, for each of these questions, plug in the given value of the independent variable for x.

Independent variable equal to 10: 0.1*10 + 5 = 6

Independent variable equal to 50: 0.1*50 + 5 = 10

Independent variable equal to 120: 0.1*120 + 5 = 17

Classify the system and identify the number of solutions.
3x + 5y + 4z = −11
2x − 4y − z = −11
4x + 3y − 2z = 11

Answers

Answer:

Hello,

Step-by-step explanation:

Only one solution: x=-2, y=3,z=-5

Answer:

consistent, independent; one

Step-by-step explanation:

The solution is (−2, 3, −5). Because the system has one solution, it is consistent and independent.

a bricklayers assistant starts building a wall laying 50 bricks per hour. Two hours later the master bricklayer joins the assistant and both lay bricks. The master bricklayer lays 80 bricks per hour. write an equation stating that the assistant and the master have laid the same number of bricks. how long has each one worked when they have laid the same number? ​

Answers

Answer:

80t = 50(t+2)master: 3 1/3 hoursassistant: 5 1/3 hours

Step-by-step explanation:

Given an assistant bricklayer laying 50 bricks an hour has worked 2 hours longer than a master bricklayer laying 80 bricks an hour, you want an equation stating they have laid the same number of bricks. You also want to know how long each has worked.

Rate and output

The output of each bricklayer is the product of the rate at which they lay bricks and the time for which they do it. If t is the time spent by the master bricklayer, their output will be 80t. The time spent by the assistant will be (t+2) hours, and their output will be 50(t+2).

Here is the equation that says their output is the same:

  80t = 50(t+2)

Time

Solving the equation for t, we have ...

  80t = 50t +100

  30t = 100 . . . . . . . . . subtract 50t

  t = 3 1/3 . . . . . . . divide by 30

The master bricklayer has worked 3 1/3 hours when they have laid the same number of bricks.

The assistant bricklayer has worked 5 1/3 hours at that time.

__

Additional comment

Each will have laid (80)(3 1/3) = 266 2/3 bricks.

4x + 3 = 18 - x help please

Answers

Answer:

the answer is x=3

Step-by-step explanation:

Answer:

Please mark my answer as the brainliest, it would mean a lot to me

x = 5

Step-by-step explanation:

4x + 3 = 18 - x

3x + 3 = 18

3x = 15

x = 5

The annual attendance at the amusement park is initially 2 million people and is increasing at 3% per year. The park’s annual food supply is initially adequate for 4 million people and is increasing at a constant rate adequate for an additional 0.2 million people per year.
a. Write the equation that represents the food supply. Write the equation represents the park attendance.
The equation that represents food supply is
b. Based on these assumptions, in approximately what year will the amusement park first experience shortages of food?

c. If the park doubled its initial food supply and maintained the rate of increase of 0.2 million people per year, would shortages still occur? In approximately which year?

d. If the park doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur? After how many years would the food supply run out?

Please show work. I will mark brainliest.

Answers

Answer:

[tex]\textsf{a)} \quad f(t) = 4+0.2t \:\: \textsf{ and }\:\:A(t)=2(1.03)^t[/tex]

b)  77 years

c)  86 years

d)  110 years

Step-by-step explanation:

Part (a)

Given:

Initial food supply adequacy = 4 million peopleConstant annual growth rate = 0.2 million people

As the food supply grows at a constant rate of being adequate for an additional 0.2 million people per year, it can be expressed as a linear function:

[tex]f(t) = 4+0.2t[/tex]

where:

f(t) = annual food supply (in millions of people).t = time (in years).

Given:

Initial attendance = 2 million peopleAnnual growth rate = 3%

As the annual attendance increases by 3% per year, it can be expressed as an exponential function:

[tex]A(t)=2(1.03)^t[/tex]

where:

A(t) = annual attendance (in millions of people).t = time (in years).Part (b)

Graph the two functions (see attached) and locate the value of t for which A(t) > f(t) for the first time.

From inspection of the graph, the two functions intersect at t ≈ 77.  So after approximately 77 years the food supply will not be enough for the number of people attending the amusement park.  Therefore, after approximately 77 years, the park will first experience shortages of food.

Part (c)

If the park doubles its initial food supply and maintains the rate of increase of 0.2 million people per year, the new equation would be:

[tex]f(t) = 8+0.2t[/tex]

Again, graph the new function against A(t) and find the point where the two functions intersect.  A(t) = f(t) at approximately t = 86 so the park will first experience food shortages after 86 years.  So doubling the initial food supply delays the eventual food shortage by only c. 9 years.

Part (d)

If the park doubled the rate at which its food supply increases in addition to doubling its initial food supply, the new equation would be:

[tex]f(t) = 8+0.4t[/tex]

Again, graph the new function against A(t) and find the point where the two functions intersect.  A(t) = f(t) at approximately t = 110 so the park will first experience food shortages after 110 years.  So doubling the initial food supply and doubling the rate delays the eventual food shortage by only c. 33 years compared to the initial parameters.  Shortages would still occur, but it would be later in approximately 110 years' time.

Simplify the expression

Answers

Answer:

-8

Step-by-step explanation:

2x/7 =

2(12)/-3 =

24/-3 =

-8

Answer:

-8

Explanation:

Given expression:

[tex]\rightarrow \sf \dfrac{2x}{y}[/tex]

when  x = 12, y = -3

Substitute values inside expression:

[tex]\rightarrow \sf \dfrac{2(12)}{-3}[/tex]

multiply

[tex]\rightarrow \sf \dfrac{24}{-3}[/tex]

simplify

[tex]\rightarrow \sf -8[/tex]

The graph of the function y = x^3 + ax^2 + b has a local minimum point at (4, -11). Find the coordinates of the local maximum. Answer: (0, 21)

Answers

Answer:

(0, 21)

Step-by-step explanation:

Stationary points occur when the gradient of a graph is zero.

Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.

Differentiate the given function:

[tex]\begin{aligned}y & = x^3+ax^2+b\\\implies \dfrac{\text{d}y}{\text{d}x}&=3 \cdot x^{3-1}+2 \cdot ax^{2-1}+0\\\implies \dfrac{\text{d}y}{\text{d}x}& = 3x^2+2ax\end{aligned}[/tex]

Set the differentiated function to zero:

[tex]\begin{aligned} \dfrac{\text{d}y}{\text{d}x}& =0\\ \implies 3x^2+2ax & = 0 \\ \implies x(3x+2a)&=0\end{aligned}[/tex]

Therefore the stationary points occur when:

[tex]\implies x=0[/tex]

[tex]\implies 3x+2a=0 \implies x=-\dfrac{2}{3}a[/tex]

There is a stationary point at (4, -11), therefore substitute x = 4 into the expression for x and solve for a:

[tex]\begin{aligned}x & = 4\\\implies -\dfrac{2}{3}a & = 4\\a & = -\dfrac{3}{2}(4)\\a & = -6\end{aligned}[/tex]

Substitute the found value of a and the point (4, -11) into the function and solve for b:

[tex]\begin{aligned}y & = x^3 + ax^2 + b\\\implies -11 & = (4)^3+(-6)(4)^2+b\\ -11 & = 64-96+b\\b & = -11-64+96\\ b & = 21\end{aligned}[/tex]

Therefore, the function is:

[tex]\boxed{y=x^3-6x^2+21}[/tex]

The other stationary point is when x = 0.  Therefore, to find the coordinates of this point, substitute x = 0 into the function:

[tex]\begin{aligned}y & =x^3-6x^2+21\\x=0\implies y & =(0)^3-6(0)^2+21\\ y & =21 \end{aligned}[/tex]

Therefore, the coordinates of the other stationary point are (0, 21).

To determine if a stationary point is minimum or maximum, differentiate the function again:

[tex]\begin{aligned}y & =x^3-6x^2+21\\\implies \dfrac{\text{d}y}{\text{d}x} & = 3x^2-12x\\\implies \dfrac{\text{d}^2y}{\text{d}x^2} & = 6x-12\\\end{aligned}[/tex]

Substitute the x-coordinate of the stationary point into the second derivative:

[tex]\begin{aligned} \dfrac{\text{d}^2y}{\text{d}x^2} & = 6x-12\\x=0 \implies \dfrac{\text{d}^2y}{\text{d}x^2} & = 6(0)-12= -12 \\\end{aligned}[/tex]

[tex]\textsf{As $\dfrac{\text{d}^2y}{\text{d}x^2} < 0$, stationary point $(0,21)$ is a maximum.}[/tex]

Differentiation Rules

[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\dfrac{\text{d}y}{\text{d}x}=nax^{n-1}$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{4cm}\underline{Differentiating a constant}\\\\If $y=a$, then $\dfrac{\text{d}y}{\text{d}x}=0$\\\end{minipage}}[/tex]

A point A (x, y) is translated 7 units to the left and 2 units up. What is the mapping to the new point A’?
(x+2, y+7)
(x-7, y+2)
(x+2, y-7)
(x+7, y+2)

Answers

Answer:  Choice B

Reason:

7 units to the left means x becomes x-7

2 units up means y becomes y+2

Therefore, the old preimage (x,y) translates or shifts to the new image (x-7, y+2)

Example:

[tex](\text{x},\text{y}) = (3,5)\\\\(\text{x},\text{y})\to(\text{x}-7,\text{y}+2)\\\\(3,5)\to(3-7,5+2)\\\\(3,5)\to(-4,7)\\\\[/tex]

The preimage (3,5) moves to (-4,7) after shifting 7 units left and 2 units up.

Write
4/11
as a decimal.
O 0.36
0.36
0.036
0.36

Answers

Answer:

0.36

Step-by-step explanation:

If f(x) = 3x2 – 2x + 4 and g(x) = 5x2 + 6x – 8, find (f +g)(x).

Answers

Answer:

[tex](f+g)(x)=8x^{2} +4x-4[/tex]

Step-by-step explanation:

[tex](f+g)(x)=3x^{2} +5x^{2} -2x+6x+4-8=8x^{2} +4x-4[/tex]

Hope this helps

A student does an experiment in a lab on the boiling point of water. In the 3 trials, the student gets the temperatures of 99.2, 99.5, 100.2 degrees C. Are these measurements:

Question 2 options:

Accuracy


Neither precision nor accuracy


Both precision and accuracy


Precision

Answers

The measurements are precise. Therefore, the correct option is D.

What is precision?

It should be noted that precision simply means how close a test is when it's repeated.

On the other hand, it should be noted that accuracy simply means how close the results are to the standard value.

Therefore, when the student does an experiment in a lab on the boiling point of water. In the 3 trials, the student gets the temperatures of 99.2, 99.5, 100.2 degrees, they're precise.

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2. Select the polynomial functions for which (x+3) is a factor. Select all that apply. (2
f(x)=x²-12x³ +54x² - 108x+81
f(x)=x²-3x³-x+3
f(x)=x+2x¹-23x³-60x²
f(x)= x³ +5x²-3x³-29x²+2x+24

Answers

The polynomial functions for which (x+3) is a factor

A polynomial of degree n is a function of the form

f(x) = anx

n + an−1x

n−1 + . . . + a2x

2 + a1x + a0

where the a is a real number (sometimes called the coefficients of the polynomial). Although

this general formula might look quite complicated, particular examples are much simpler. For

example,

f(x) = 4x

3 − 3x

2 + 2

is a polynomial of degree 3, as 3 is the highest power of x in the formula. This is called a cubic

polynomial, or just cubic.

Theorem Polynomial Division: Suppose d(x) and p(x) are nonzero polynomials were

the degree of p is greater than or equal to the degree of d. There exist two unique polynomials,

q(x) and r(x), such that p(x) = d(x) q(x) + r(x), where either r(x) = 0 or the degree of r is

strictly less than the degree of d.

so, if we put x=-3 then f(x) must be equal to zero

here no function satisfies of none of the option is correct for [x+3] factor

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(x +3) is a factor of the function f(x)= x³ +5x²-3x³-10x²+2x-3.

Here, we are given 4 functions. If (x+3) is a factor of any of these equations, then x = -3 and y = 0 must be a solution. Let us check each function one by one-

1. f(x) = x²-12x³ +54x² - 108x+81

putting x = -3, we get-

f(-3) = -3²-12(-3)³ +54(-3)² - 108(-3)+81

= 9+324+486+324+81

= 1,224

Thus, (x +3) is not a factor.

2. f(x)=x²-3x³-x+3

putting x = -3, we get-

f(-3) = -3²-3(-3)³-(-3)+3

= 9+81+9+3

= 102

Thus, (x +3) is not a factor.

3. f(x)=x+2x¹-23x³-60x²

putting x = -3, we get-

f(-3) = -3+2(-3)¹-23(-3)³-60(-3)²

= -3-6+621+540

= 1,152

Thus, (x +3) is not a factor.

4. f(x)= x³ +5x²-3x³-10x²+2x-3

putting x = -3, we get-

f(-3) = -3³ +5(-3)²-3(-3)³-10(-3)²+2(-3)-3

= -27+45+81-90-6-3

= 0

Thus, (x +3) is a factor of the function f(x)= x³ +5x²-3x³-10x²+2x-3.

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Please help I will give anyone brainliest

Answers

Answer:

1672.50 = 37.75x + 1068.50

x = 16

There were 16 players brought to the tournament.

Step-by-step explanation:

y = mx + b

y= the total cost

m = cost of each meal

x = the number of players

b = cost of the bus

Plug in what you know and solve for x

1672.50 =  37.75x + 1068.50  Subtract 1068.50 from both sides.

604 = 37.75x  Divide both sides by 37.75

16 = x

Equation: 1068.50 + 37.75x =1,672.50

Answer: X= 16

If 1,672.50 is our total it will go behind the equal sign. 37.75x and 1068.50 must be added together to help us receive our total.

Our written equation should look like this

1068.50 + 37.75x =1,672.50

X is the number of players on the team.To find out we must first subtract the amount of money spent on the bus, from the total amount spent.

1,672.50-1068.50 is 604. This means our equation now looks like this

37.75x=604. The next and final step is to divide 37.75 into 604.

604/ 37.75 is 16. Which means that there are 16 players on the team.

I hope this helps & Good luck.

Find the average rate of change of the function f(x) = x² + 4x from x₁ = 3 to x₂ = 5.

Answers

The average rate of change of the given function is 12.

The average rate of change of function f on interval [a,b] is:

f(b) -f(a)/b-a

we have interval [x₁,x₂]

[x₁,x₂] = [3,5]

f(3) = x²₊4x

f(3) = 3²+4(3)

f(3) = 21

f(5) = x²₊4x

f(5) = 5²+4(5)

f(5) = 45

f(x₂) -f(x₁)/x₂-x₁

⇒ 45-21/5-3

= 24/2

= 12

The average rate of change of function f(x) = x²+4x on interval [3,5]

is 12.

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Let f (x) = 3x2 − 2x + 4. Evaluate f (a + h) and simplify your answer as much as possible.

Answers

The expression f(x) = 3 · x² - 2 · x + 4 evaluated at x = a + h is equal to the expression f(x) = 3 · a² + 6 · a · h + 3 · h² - 2 · a - 2 · h + 4.

How to evaluate and simplify a quadratic equation

In this question we find a quadratic equation, which has to be evaluated at x = a + h and simplified afterwards. Then, the complete procedure is shown below:

f(x) = 3 · (a + h)² - 2 · (a + h) + 4

f(x) = 3 · (a² + 2 · a · h + h²) - 2 · a - 2 · h + 4

f(x) = 3 · a² + 6 · a · h + 3 · h² - 2 · a - 2 · h + 4

The expression f(x) = 3 · x² - 2 · x + 4 evaluated at x = a + h is equal to the expression f(x) = 3 · a² + 6 · a · h + 3 · h² - 2 · a - 2 · h + 4.

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Solve.

⎧⎩⎨⎪⎪2x−y+2z=−6−3y+z=−22x−3z=4

Enter your answer, in the form (x,y,z), in the boxes in simplest terms.

Answers

The solution is (x, y, z) = (-1, 0, -2)

Given equations are:

2x−y+2z=−6 ---------------(1)

−3y+z=−2 ------------------(2)

2x−3z=4 -------------------(3)

From (2), z = -2+3y

Substitute this into (1) and (3)

(1)⇒ 2x-y+2(-2+3y) = -6

⇒ 2x+5y-4=-6

⇒2x+5y = -2

and

(3) ⇒ 2x-3(-2+3y)=4

⇒ 2x-9y+6 = 4

⇒ 2x-9y=-2

Now solve 2x+5y = -2 and 2x-9y=-2

Subtracting the equations above,

14y = 0

y=0

Then from 2x-9y=-2, x = -1

From (2),z = -2+3y

z = -2

So the solution is (x, y, z) = (-1, 0, -2)

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write an expression to show the total number of songs on Iris's playlist after w weeks

Answers

120 + 4w is the expression to show the total number of songs on Iris's playlist after w weeks.

She total ahs 120 songs already

She downloads or adds 4 songs every week

An expression to show the total number of songs on Iris's playlist after w weeks is:

120 + 4w

What is an mathematical expression?

An expression or mathematical expression is a limited combination of symbols that is well-formed according to context-dependent norms. To help identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.

Many authors differentiate between an expression and a formula, with the former referring to a mathematical item and the latter referring to a statement about mathematical objects.

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I can’t find a way to flip the number and to swap it as well

Answers

Answer:

Reflect over the x axis and than turn 90 degrees clockwise about the origin.

The temperature at
7:00 P.M is 18°F. At
7:00 A.M. the next
day, the temperature
is -12°F. What integer
represents the change
in temperature?

Answers

Answer: -30 degrees fahrenheit

Step-by-step explanation: 18 + (-12) = -30

Name a point non-coplanar to plane K

Answers

W is the point which is non coplanar to plane k .

WHAT IS A COPLANAR/NON-COPLANAR POINT ?

A group of points that are in the same plane are said to be coplanar. A coplanar line connects any two or three points. It's possible that four or more points are coplanar.

The coplanar points A, B, C, and D are displayed on the left side of the above figure. Additionally, there are other sets of coplanar points in the box to the right. For instance, the left side of the box's left side is the plane that contains the coplanar points P, Q, X, and W. There are four coplanar points on each of the box's six faces, however they are not the only coplanar point groups. Points Q, X, S, and Z, for instance, are coplanar despite the fact that the plane containing them isn't depicted.

Non-coplanar points are a collection of points that are not all located on the same plane.

Points P, Q, X, and Y in the previous figure are not coplanar. Q, X, and Y are located on the box's top, and P, Q, and X are located on the box's left side, however no flat surface has all four points.

CALCULATION

since from the figure we can find out that except two points W , Y all the points are on the plane K .

so according to question and given figure we conclude that one of the point which in non coplanar to K is W.

points highlighted in the figure is non coplanar to point k .

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A total of 200 and a difference of 72

Answers

According to the solving the total and the difference of the numbers:

total = 136 + 64

difference  = 64

Difference in Math Definition?

Mathematical difference is the outcome of one of the key operations, which is the subtraction of two numbers. It reveals the margin of difference between two numbers.

How do we find the difference?

Subtract the largest number from the lowest number to determine the difference between two integers. The difference between these two numbers is the product of this sum. As a result, there are 55 between the numbers 45 and 100.

According to the given data:

Let the numbers be x and y

Given,

x+y = 200_____(1)

x-y = 72_____(2)

Add above 2 eq.

2x= 272

x= 136

Substitute the value of x in eq 1,we get

136+y = 200

y = 64

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nate works at a grocery store. he has 7 1/2 pounds of rasins. heis splitting them into 1/8 pound packages. how many packages can he make

Answers

Answer:

Nate can make 60 packages.

Step-by-step explanation:

7 1/2 is equivalent to 7 4/8, or 60/8

Divide 60/8 by 1/8 and you get 60.

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